DESCRIPTION (provided by investigator): This application constitutes a renewal application for the previously funded study entitled "Analytic Methods: Environmental/Reproductive Epidemiology". The initial funding cycle facilitated a productive collaboration, and these efforts have revealed promising new directions for research to more fully encompass the multiple challenges posed by exposure and reproductive health data collected under motivating studies such as the Michigan PBB Studies (MIPBB) and the Mount Sinai Study of Women Office Workers (MSSWOW). As in many longitudinal studies, exposure assays utilized in the MIPBB underwent an evolution over time so that data obtained via the original and more recent assays are recorded at different levels of resolution. In particular, data obtained earlier in the study were primarily "heaped", due to assay limitations that effectively led values to be rounded to the nearest integer. Proper analysis of the longitudinal data should attribute the correct level of resolution to each data point, based on the assay used to record it. In epidemiologic studies, it is also common to observe highly skewed exposure data. The simultaneous features of heavy skewness, detection limit issues, changing assay resolution over time, and heaping due to rounding require flexible and innovative modeling, with the ultimate aim of improved prediction and valid determination of associations between exposure and reproductive health outcomes (Aim 1). Our research to date motivated by the MSSWOW study has identified new avenues of research into the modeling of time-to-pregnancy and menstrual cycle length data. In such studies, time-to-pregnancy is typically recorded in terms of a number of cycles as opposed to being measured in days or weeks, so that methods for discrete data survival analysis are required. Modeling innovations are needed in order to relate environmental exposures and other covariates to fertility in such contexts (Aim 2). Repeated menstrual cycle length data tend to be characterized by heterogeneity not only in average length, but in the level of variability as well. This motivates a need for flexible modeling and improved methods for classifying women into menstrual cycle length and variability subgroups, and brings attention to potential misclassification error (Aim3). This renewal application continues to seek improved analytic methods for epidemiologic research by means of an effective balance between statistical theory and application in the environmental and reproductive health areas. We consider both parametric and semi-parametric approaches, noting that both have their advantages in this context and that each approach has the potential to inform and augment the other. While intended to be of direct benefit to the motivating studies, the methods to be developed address issues that are common and fundamental enough to make them of broader interest in statistical and epidemiologic practice. PUBLIC HEALTH RELEVANCE Environmental exposures can have a major impact on various aspects of public health, including women's reproductive health. This application aims to address multiple unique challenges in the analysis of exposure and reproductive health outcome data stemming from two landmark motivating studies. The statistical methods to be developed will also have broader implications toward public health studies that collect exposure and outcome data over time.